There are three types of coins that have different probabilities of landing heads when tossed:

Type A coins are fair, with probability 0.5 of heads 7 Type B coins are bent and have probability 0.6 of heads 7 Type C coins are bent and have probability 0.9 of heads Suppose I have a drawer containing 5 coins: 2 of type A, 2 of type B, and 1 of type C. I reach into the drawer and pick a. coin at random. Without showing you the coin I ip it once and get heads (Le. event D). What is the probability it is type A (i.e. P(H :AlD))? Type B [i.e. P(H : B|D))? Type C (i.e. P(H : C|D))? Fill out table below with your answers. hypothesis prior likelihood posterior H P(H) P(DlH) P(H|D) A B